Quickly Multiply by 21

Rule for multiplying any number by 21

Start from left. Double the first digit and add it to left side neighboring digit. Repeat the steps for subsequent digits. The last number will be same as the last number of the multiplied number.

 

This rule is very much like the shortcut for multiplying by 11. Since 21 is sum of 11 and 10, it does belong to the same family of short cuts.

Let’s understand the whole concept with an example. Let’s multiply 5392 by 21.

The first digit of the answer will be equal to twice the first digit of 5392. To make the rule consistent assume there is a zero before the number.

So it looks like 05392

0 + (5 x 2) = 10

As stated in the rule above, next, add the first digit of the given number, 5, to twice the second digit, 3.

5 + (2 x 3) = 11

Since we must have a single digit at each step, the tens place of the result above will be carried over and added to the previous number.

1  | (0 +1) | 1 = 111

The first 3 digits up to this point are 111

The next digit is obtained by adding 3 to twice of 9

3 + (2 x 9) = 21

Thus the first four digits of the answer are -

1  | 1  |  (1 + 2)  | 1 = 1131   (carried over 2 added to the last digit of 111 )

The next digit is obtained by adding 9 to twice of 2

9 + (2 x 2) = 13

Thus the first five digits of the answer are -

1  | 1  | 3  |  (1+1)  |  3

The last digit of the answer will be same as the last digit of the number itself.

Hence, in this case last digit will be 2.

Therefore the answer is 113232

Note: ” | ” is used as a partition between two digits.

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